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\begin{abstract}
Summary of our discussion.
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\section{Our Discussion so far (Dt: March 22, 2012}


(C:Chinmoy, R:Ravi)\\

Dear Ravi, dear Chinmoy,\\

I am summarising all the discussions that we have had so far:

1) Our motive (as per C's write-up) was to develop/harvest a network in a way that the network topology facilitates the owner of the network to spread information to all  the nodes (or most of them) in the network. I thought we could use the notations as used in Narahari's paper. Infecting some $k$ nodes in the network should ensure that $\lambda$ percentage of the nodes must get infected in time step $t$. If C and R are ok with this, we will stick to this language. Let us call a network which is harvested in accordance with our method as having reached the {\it harvested-state}.

2) I discussed separately with C day before and with R yesterday about the difficulty in fetching a benevolent data for our experiment. Assuming we have a harvesting technique that gives us the desired network, how do we put this method to use given some real world data? 

3) I discussed with R that facebook apart from suggesting friends to its users (let us call this Automated Friend Suggestion -AFS- henceforth) also enables a user X to recommend two of his friends Y and Z to each other. It is believed that facebook generates more friendships this way than by AFS.

4) To increase the credibility of our work, we should ensure that our technique is applicable to an existing social network. By that I mean, we should be able to consider a given network and take it to the harvested state. R told me yesterday that we could consider some real world networks and show that we can plug in a few extra edges and bring it to the harvested state.

 5) I independently discussed with R and C that a nice definition for harvested state would be the following:

A graph $G$ is said to be in $\beta-$harvested state, if the removal of the top $\beta$ high degree nodes would give us a big component with the degree distribution obeying power law (with a desired exponent). 

This would translate to the network continuing to stay robust despite the removal of the top few high degree nodes which by the virtue of powerlaw continues to enable the owner of the network to transmit information by infecting the top few nodes.    

R told me that it would be difficult for us to work on the theoretical front with the above definition in mind.

6) As I see, we have two High priority questions:

a) When do we call a network as having reached the harvested state?
b) How do we validate our method using real world data?

-Sudarshan

PS: I will add a few references to our google-code project very soon.

\section{March 25, 2012}


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